× ENGR 102-Homework 3. https ecampuswww.edu/bbcswebdav/pid-4939 181-dt-content-r

Question

× ENGR 102-Homework 3. https ecampuswww.edu/bbcswebdav/pid-4939 181-dt-content-rid-415568131 1805 ENGRT Mr. Spada ENGR 102: Engineering Problem Solving II Homework 3: 1D Arrays and Plots Solve all problems in a single seript file in Matlab. Ensure that your file is saved as LastName_FirstName HW3 before submitting, Submit your file to eCampus by Sunday 7/8/2018 at 11:59 PM. Create sets of reference values for sine, cosine, and tangent for angles ranging from 0 to 2?. Do this in two ways: (1) use a spacing of 0.5 radians, and (2) use 10 linear-spacedl points. Use output functlons to display the values in a manner which will be easily read by the user 1. 2. A spring's displacement in the x direction is defirned by the fallowing equation: where: x is the displacement of the spring at a given time, t; A is the maximunm displacement, and is the angular frequency [dependent upon the spring constant) Find the displacement of the spring from times ranging from 0 to 20 seconds at one second intervals. The maximum displacement af tho spring is known to be 3 inches. The angular frequency is known to be 0.5 radians per second.

Explanation / Answer

Please find the required MATLAB function as:

%=================================================

function [ ] = cannonball_distance( v0 )
g=9.81; % gravitational acceleration
angles = 0:pi/32:pi/2; % Vector of angles to verify distances
max_dist=0; % Initialization
for i=angles     % This loop calculates the distances for each angle and keeps only the maximum
    distance = (v0^2)*sin(2*i)/g;
    if(distance>max_dist)
        max_dist=distance;
        max_angle=i;
    end
    fprintf(' At angle = %f , distance = %f ',rad2deg(i),distance);
end
fprintf(' The cannonball achieves maximum distance of %f meters at the angle of %f degrees!! ',max_dist,rad2deg(max_angle));
end

%============================================

Sample output:

>> cannonball_distance(125)

At angle = 0.000000 , distance = 0.000000

At angle = 5.625000 , distance = 310.732547

At angle = 11.250000 , distance = 609.523816

At angle = 16.875000 , distance = 884.891426

At angle = 22.500000 , distance = 1126.253156

At angle = 28.125000 , distance = 1324.333608

At angle = 33.750000 , distance = 1471.520662

At angle = 39.375000 , distance = 1562.158003

At angle = 45.000000 , distance = 1592.762487

At angle = 50.625000 , distance = 1562.158003

At angle = 56.250000 , distance = 1471.520662

At angle = 61.875000 , distance = 1324.333608

At angle = 67.500000 , distance = 1126.253156

At angle = 73.125000 , distance = 884.891426

At angle = 78.750000 , distance = 609.523816

At angle = 84.375000 , distance = 310.732547

At angle = 90.000000 , distance = 0.000000

The cannonball achieves maximum distance of 1592.762487 meters at the angle of 45.000000 degrees!!

%==========================================================

NOTE:

1) The function file must be the same as the name of the function. For example, in the code above, it must be saved as "cannonball_distance.m"

2) To call the function use: cannonball_distance(<initial velcity value>) from the MATLAB command shell.

Hope this helps! ******************* Please Thumbs Up! *******************

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